Which of the following numbers is a factor of 66? ${5,6,7,9,12}$
Solution: By definition, a factor of a number will divide evenly into that number. We can start by dividing $66$ by each of our answer choices. $66 \div 5 = 13\text{ R }1$ $66 \div 6 = 11$ $66 \div 7 = 9\text{ R }3$ $66 \div 9 = 7\text{ R }3$ $66 \div 12 = 5\text{ R }6$ The only answer choice that divides into $66$ with no remainder is $6$ $ 11$ $6$ $66$ We can check our answer by looking at the prime factorization of both numbers. Notice that the prime factors of $6$ are contained within the prime factors of $66$ $66 = 2\times3\times11 6 = 2\times3$ Therefore the only factor of $66$ out of our choices is $6$. We can say that $66$ is divisible by $6$.